Intersectionality is intrinsically about grouping people by identity categories, and then dicing those groups against each other (black|white x straight|bi|gay = black-straight | black-bi | black-gay | white-straight | white-bi | white-gay; now think about all six groups separately, and think about how people's experiences are shaped by which of the six boxes into which they fall).

If you fail to do this and instead consider "everyone's unique experiences", you're talking about individualism, not intersectionality.

You might be marginalized because you have a habit of blinking too much when you talk. "That's not really fair; blinking doesn't affect job performance" is the individualist perspective. "Hyperblinkers are an oppressed minority, and we need to consider separately the oppression of male hyperblinkers and female hyperblinkers and genderfluid hyperblinkers" is the intersectional perspective.

Intersectionality was necessarily this because it was founded as a legal strategy to prove patterns of discrimination.